Infants were presented with an object that moved into reaching space on a path that was either continuously visible or interrupted by an occluder. Infants’ reaching was reduced sharply when an occluder was present, even though the occluder itself was out of reach and did not serve as a barrier to direct reaching for the object. We account for these findings and for the apparently contrasting findings of experiments using preferential looking methods to assess infants’ object representations, by proposing that (a) object representations increase in precision over the infancy period, and (b) the precision of object representations varies in common ways at all ages as a function of object visibility and task demands.